Results: A total of 300 subjects (139 men and 161 women) of various ethnicities with a mean (?????SD) body mass index (in kg/m2) of 25.1 ?? 5.4 met the study entry criteria. The mean conceptual model???derived TBK-SM ratio was 122 mmol/kg, which was comparable to the measurement-derived TBK-SM ratios in men and women (119.9 ?? 6.7 and 118.7 ?? 8.4 mmol/kg, respectively), although the ratio tended to be lower in subjects aged ??????70 y. A strong linear correlation was observed between TBK and SM (r = 0.98, P < 0.001), with sex, race, and age as small but significant prediction model covariates.
I think I understand what the p means (like percent change or something?) but what does the r mean? Would an r of 1 mean a 1:1 relationship in the data-set if it were graphed?
asked byStephen_4 (10989)
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on July 09, 2013
at 04:32 PM
what they are presenting is actually r-squared, not r.
R-Squared is the coefficient of determination in statistics. It is the measure of how well least squares measures the outcome.
In English, it is used, with linear regression, as a measure of how well a model predicts observed outcomes. the number is percentage of variation that can be explained by regression. The higher the r-squared, the better the model. and r-squared of 1 means that the model perfectly predicts observations (and thus the real world).
The p-value is, essentially, a measure of the likelihood that the observed value is extreme given that the null hypotehsis is true. The p-value, along with chi square, allow one to determine likelihood of statistical significance. A p-value of 0.05 between two populations would say that there is a 95% likelihood that the change between the two populations is a real change, and not a random artifact.
So, in your scenario, (r-squred=.98) all but 2% of the variation could be explained with regression. This a good result, we typically like to see 3-5 9's for computational measures, but in human models a .98 is very strong. This means that the model can be used to predict, for example, the TBK-SM ratio for a random person given the same entry criteria and given the same protocol within 2%.
The p<0.001, means that there is a very strong statistical likelihood that these findings are accurate and not a result of randomness. This is an absurdly low p-value. Given the subject size, 300, I would suspect bias in experimental design (but that's just a shot in the dark as I have not read the study).
Also it's always important to question statistical significant and actual significance. Over the course of 10 years, if one diet caused it's population to loose 1 pound more than another diet. While it may be a statistically significant result, in practice 1 pound difference in not significant.
Again, I have not looked at this study in particular, but just a few things that I look for in all studies.
on July 09, 2013
at 06:39 PM
CD's answer is mostly good, but two points need correction.
First of all, r-squared does represent the amount of variation that is explained by the model. However, unless a paper explicitly says they're reporting
r^2, they are NOT reporting
r. You need to square it yourself to find out what the actual meaning of the correlation is. One reason they do this is that it's important to know whether a correlation is positive or negative, but after you square it it's always positive.
p is not a measure of how likely it is that your results are true. This is a very common misunderstanding and even a lot of scientists get drawn into it. Apologies in advance for the lecture, but this is kind of hard to explain. What p tells you is this:
If the two variables weren't actually related, what is the probability you'd get a result like this due to random chance?
For example, it's theoretically possible that smoking doesn't actually cause lung cancer. Maybe it's just that by a random fluke of chance, every study that's ever shown a relation just happened to recruit a bunch of nonsmokers who got really, really lucky with regards to cancer and a bunch of smokers who were astronomically unlucky. Just like it's possible that you could flip a fair coin and have it come up heads 1000 times in a row. You can calculate the odds of that happening, and obviously they're very low -- that's what the p value represents.
A p value tells you how UNlikley your results are, in a theoretical world where the results aren't actually true. It DOESN'T tell you how likely it is that your result actually is true.
For example, imagine that I run a study and find that people who drink 10 beers a day are healthier and live longer than people who drink 0-2. My result has p=.05, meaning that there's only a 5% chance I would have found a difference that big by chance, if drinking actually didn't affect your health at all.
Would you conclude from this that there's a 95% chance that drinking 10 beers a day is good for you? Or would you still think that it's probably bad, and assume that my results were the equivalent of rolling a 20 on a 20-sided die -- something that's not common, but still totally possible?
on July 09, 2013
at 04:29 PM
Someone who's taken more than intro stats can better answer this, but I believe r is the correlation coefficient, which is a measurement of strength of correlation (-1 < r < 1, r=1 is a perfectly linear positive association). P-value is a little more complicated, but in this case would basically be the probability of finding this particular positive relationship between TBK and SM if in actuality there was NO relationship at all between TBK and SM. Whatever those are. Whether the p-value is above or below a certain threshold (often .05, depending on the discipline) determines the the significance of the result.